Towards Rock-paper-scissors patterns in the Optional Public Goods Game under random mobility

TL;DR

This paper demonstrates that simple random mobility in an optional public goods game can produce rock-paper-scissors patterns, highlighting their role in maintaining cooperation and species diversity.

Contribution

It shows that RPS patterns emerge with minimal assumptions about neighborhood structure, and introduces a new method to quantify RPS density for finite size analysis.

Findings

RPS patterns occur with simple random mobility in sparse lattices.

A novel quantitative method for RPS density is proposed.

RPS patterns are crucial for understanding cooperation and species conservation.

Abstract

Social dilemmas concern a natural conflict between cooperation and self interests among individuals in large populations. The emergence of cooperation and its maintenance is the key for the understanding of fundamental concepts about the evolution of species. In order to understand the mechanisms involved in this framework, here we study the Optional Public Good Games with focus on the effects of diffusive aspects in the emergent patterns of cyclic dominance between the strategies. Differently from other works, we showed that rock-paper-scissors (RPS) patterns occur by introducing a simple kind of random mobility in a lattice sparsely occupied. Such pattern has been revealed to be very important in the conservation of the species in ecological and social environments. The goal of this paper is to show that we do not need more elaborated schemes for construction of the neighbourhood in the game to observe RPS patterns as suggested in the literature. As an interesting additional result, in this contribution we also propose an alternative method to quantify the RPS density in a quantitative context of the game theory which becomes possible to perform a finite size scaling study. Such approach can be very interesting to be applied in other games generically.